Synthesis Lectures on Mathematics & Statistics An Introduction to Partial Differential Equations

This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter. In addition, this book: Introduces methods and techniques for solving first and second order PDEs Presents the main four PDEs (the advection equation, the diffusion equation, Laplace’s equation, and the wave equation), which are considered to be the cornerstone of Applied Mathematics Contains numerous exercises throughout to facilitate learning and has been class tested over the past 10 years